Theorems · Theorem · linear algebra
Matrix.GeneralLinearGroup.map_swap
∀ {R : Type u_1} {n : Type u_2} [inst : CommRing R] [inst_1 : DecidableEq n] [inst_2 : Fintype n] {S : Type u_3}
[inst_3 : CommRing S] (f : R →+* S) (i j : n),
(Matrix.GeneralLinearGroup.map f) (Matrix.GeneralLinearGroup.swap R i j) = Matrix.GeneralLinearGroup.swap S i j- Defined in
- Mathlib.LinearAlgebra.Matrix.Swap
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 85 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- RingHomstatement and proof · cited by 10,189
- Fintypestatement and proof · cited by 7,736
- Matrixstatement · cited by 4,303
- MonoidHomstatement · cited by 3,629
- Matrix.GeneralLinearGroupstatement · cited by 556
- Units.extproof · cited by 86
- Matrix.GeneralLinearGroup.mapstatement · cited by 29
- Matrix.swapproof · cited by 19
- Matrix.GeneralLinearGroup.swapstatement · cited by 2
- Matrix.GeneralLinearGroup.val_map_applyproof · cited by 1
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